Useful Mathematics References
A quick index of the most-used math reference pages on Mini Physics: calculus, trigonometry, series, vectors, and differential equations.
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The core idea
On this page
This page is a quick index of math reference pages used across Mini Physics.
Use it as a tactical support page when you are solving physics and need a method quickly (not as a full course sequence). If you are stuck on a derivation, start with the “Common tasks” jumps, then move to the core reference in that topic family.
If you’re a physics undergraduate and want a “learn properly” order (not just links), use: Mathematics for Undergraduate Physics.
Who this index is for and how to use it
- Best for: A-level/H3/undergraduate learners who already know basic calculus and want fast retrieval.
- Prerequisites: algebra, trigonometric manipulation, and comfort reading formulas with symbols.
- Recommended workflow: pick one immediate task, open one core reference page, then do one worked problem before switching topics.
- Why this matters: most physics mistakes are method-selection errors, not concept errors; a curated math index reduces that friction.
Common tasks (fast jumps)
- Check units / sanity-check equations: Dimensional Analysis
- Quote results properly (uncertainty): Uncertainty & Error Propagation
- Approximate for small parameters: Taylor Series
- Convert “sin + cos” to one sinusoid: Trigonometry, Complex numbers
- Flux/circulation integrals (E&M): Vector Calculus (Integral Theorems)
Core references (most used)
Differentiation Techniques
Learn derivatives properly (rules, chain rule patterns, implicit/log differentiation).
Table of Derivatives
Derivative rules + common results (quick lookup).
Integration Techniques
Substitution, parts, partial fractions, and definite integrals (with examples).
Integration Table
Common antiderivatives and identities (quick lookup).
Taylor Series
Standard series + approximations you use everywhere in physics.
Vector Analysis
Dot/cross products and ∇ operators (grad/div/curl) with meaning + examples.
Trigonometry and complex numbers (amplitude + phase)
Trigonometry
Identities, angle formulas, and “single sinusoid” tricks.
Hyperbolic Functions
sinh, cosh, tanh identities and relationships (plus an ODE example).
Complex Numbers (Euler’s formula and phasors)
Polar form, e^iθ, and why sinusoids become easy.
UY1: Phasors & Alternating Currents
A physics application: AC circuit phase relationships and phasor diagrams.
Differential equations (modeling change)
First-order differential equations
Separable, linear, Bernoulli, homogeneous, plus worked examples and physics applications.
Second-order differential equations
Constant-coefficient methods, forcing, damping, and oscillation templates.
Multivariable and vector calculus (fields in space)
Partial derivatives
Partial derivatives, total derivative chain rule, gradients, Jacobians (change of variables).
Vector calculus (integral theorems)
Line/surface/volume integrals, Gauss’ theorem, Stokes’ theorem with examples.
Coordinate transformation under rotation
How vectors/components transform when axes rotate (active vs passive).
Linear algebra (coupled systems)
Matrices and linear algebra
Linear systems, transformations, eigenvalues/eigenvectors (with examples).
Euler–Lagrange equation
The core calculus-of-variations tool used in Lagrangian mechanics.